Upon reaching Northshore Landing, you will find several Thalmor agents led by an elf called Ancarion. It is possible to use diplomacy and speak with the leader, whereupon three choices become present:

Persuade - If you manage to pass a persuasion check, you can convince Ancarion that the blacksmith will not talk, and that they are wasting their time. Ancarion will relent and give up, giving you the map.

Intimidate - If you can intimidate the leader, he will confess that no weapon is worth dying for, and will stand down, giving you the map.

Make a Deal - If you would rather stand to make some money off of this encounter, you can convince Ancarion that giving you the map will convince the blacksmith to teach you the art of forging Stalhrim, which you can then sell to him.

Alternatively, if talking isn't your style, you can either pickpocket the map, or kill the whole lot of them and loot the map off of his dead body.